A Quantum of Variance, and the Challenge for Finance

Q-variance refers to a property of asset price behavior, where the expected variance over a period is related to price change over the same period by a simple quadratic equation, whose only parameter is a base volatility. The property was first predicted using a quantum oscillator model (the q can stand for quadratic, or quantum) but has been demonstrated empirically for a range of asset types. This paper focuses on the consequences of q-variance for topics including asset price modeling, implied volatility, and the estimation of risk. It argues that while classical finance provides a reasonable approximation to some aspects of market behavior, q-variance means that it breaks down when used to estimate volatility, so a new approach is called for.